UTA-STAR Report

Generated 2025-09-01 17:30:58

Overview

This report compares two approaches under the same preference framework: (1) piecewise linear utilities (standard UTA-STAR) and (2) a linear weighted-sum baseline. It summarizes performance, utilities, and weights per subset, with plots and equations.

How this differs from a pure weighted-sum

UTA-STAR estimates per-criterion utility functions that can be non-linear, allowing different marginal returns across the criterion range. The linear baseline constrains utilities to u_i(x)=w_i·x, i.e., straight lines through the origin with slope w_i. When utilities are strongly non-linear, UTA-STAR can fit preferences better.

Benefits

Subset: parcels_subset

Best alpha: 4 | Breakpoints: [0.00, 0.25, 0.50, 0.75, 1.00]
AvgRank (Utilities): 2194.18 AvgRank (Linear): 3674.06 Top500 (U): 11.8% Top500 (W): 11.8%

Piecewise utility functions

utility plot

Linear weights

weights bar

Piecewise equations

Count of Structures within a Quarter Mile(x) =
  if 0.00 <= x <= 0.25:  u(x) = 0.0000 * x + 0.0000
  if 0.25 <= x <= 0.50:  u(x) = 0.0000 * x + 0.0000
  if 0.50 <= x <= 0.75:  u(x) = 0.0000 * x + 0.0000
  if 0.75 <= x <= 1.00:  u(x) = 2.1886 * x + -1.6414

Very High Hazard Severity Zones % within a Half Mile(x) =
  if 0.00 <= x <= 0.25:  u(x) = 0.0000 * x + 0.0000
  if 0.25 <= x <= 0.50:  u(x) = 0.0000 * x + 0.0000
  if 0.50 <= x <= 0.75:  u(x) = 0.0040 * x + -0.0020
  if 0.75 <= x <= 1.00:  u(x) = 0.0000 * x + 0.0010

Agriculture and Fuel Break % within a Half Mile(x) =
  if 0.00 <= x <= 0.25:  u(x) = 0.0000 * x + 0.0000
  if 0.25 <= x <= 0.50:  u(x) = 0.0000 * x + 0.0000
  if 0.50 <= x <= 0.75:  u(x) = 0.0000 * x + 0.0000
  if 0.75 <= x <= 1.00:  u(x) = 0.0000 * x + 0.0000

Burn Scar % within a Half Mile(x) =
  if 0.00 <= x <= 0.25:  u(x) = 0.0774 * x + 0.0000
  if 0.25 <= x <= 0.50:  u(x) = 0.0000 * x + 0.0193
  if 0.50 <= x <= 0.75:  u(x) = 0.0000 * x + 0.0193
  if 0.75 <= x <= 1.00:  u(x) = 0.0000 * x + 0.0193

Slope (%)(x) =
  if 0.00 <= x <= 0.25:  u(x) = 0.0063 * x + 0.0000
  if 0.25 <= x <= 0.50:  u(x) = 0.0000 * x + 0.0016
  if 0.50 <= x <= 0.75:  u(x) = 0.0000 * x + 0.0016
  if 0.75 <= x <= 1.00:  u(x) = 0.0000 * x + 0.0016

WUI Coverage % within a Half Mile(x) =
  if 0.00 <= x <= 0.25:  u(x) = 0.0000 * x + 0.0000
  if 0.25 <= x <= 0.50:  u(x) = 0.0000 * x + 0.0000
  if 0.50 <= x <= 0.75:  u(x) = 0.0000 * x + 0.0000
  if 0.75 <= x <= 1.00:  u(x) = 0.0000 * x + 0.0000

Fire Behavior Fuel Model (normalized)(x) =
  if 0.00 <= x <= 0.25:  u(x) = 1.7237 * x + 0.0000
  if 0.25 <= x <= 0.50:  u(x) = 0.0000 * x + 0.4309
  if 0.50 <= x <= 0.75:  u(x) = 0.0000 * x + 0.4309
  if 0.75 <= x <= 1.00:  u(x) = 0.0000 * x + 0.4309

Subset: subset_1

Best alpha: 2 | Breakpoints: [0.00, 0.50, 1.00]
AvgRank (Utilities): 25.76 AvgRank (Linear): 29.94 Top500 (U): 100.0% Top500 (W): 100.0%

Piecewise utility functions

utility plot

Linear weights

weights bar

Piecewise equations

Count of Structures within a Quarter Mile(x) =
  if 0.00 <= x <= 0.50:  u(x) = 0.0180 * x + 0.0000
  if 0.50 <= x <= 1.00:  u(x) = 0.0000 * x + 0.0090

Very High Hazard Severity Zones % within a Half Mile(x) =
  if 0.00 <= x <= 0.50:  u(x) = 0.0000 * x + 0.0000
  if 0.50 <= x <= 1.00:  u(x) = 0.0000 * x + 0.0000

Agriculture and Fuel Break % within a Half Mile(x) =
  if 0.00 <= x <= 0.50:  u(x) = 0.0000 * x + 0.0000
  if 0.50 <= x <= 1.00:  u(x) = 0.0604 * x + -0.0302

Burn Scar % within a Half Mile(x) =
  if 0.00 <= x <= 0.50:  u(x) = 1.8988 * x + 0.0000
  if 0.50 <= x <= 1.00:  u(x) = 0.0097 * x + 0.9446

Slope (%)(x) =
  if 0.00 <= x <= 0.50:  u(x) = 0.0000 * x + 0.0000
  if 0.50 <= x <= 1.00:  u(x) = 0.0000 * x + 0.0000

WUI Coverage % within a Half Mile(x) =
  if 0.00 <= x <= 0.50:  u(x) = 0.0022 * x + 0.0000
  if 0.50 <= x <= 1.00:  u(x) = 0.0090 * x + -0.0034

Fire Behavior Fuel Model (normalized)(x) =
  if 0.00 <= x <= 0.50:  u(x) = 0.0019 * x + 0.0000
  if 0.50 <= x <= 1.00:  u(x) = 0.0000 * x + 0.0010

Subset: subset_2

Best alpha: 4 | Breakpoints: [0.00, 0.25, 0.50, 0.75, 1.00]
AvgRank (Utilities): 899.08 AvgRank (Linear): 2520.50 Top500 (U): 45.8% Top500 (W): 0.0%

Piecewise utility functions

utility plot

Linear weights

weights bar

Piecewise equations

Count of Structures within a Quarter Mile(x) =
  if 0.00 <= x <= 0.25:  u(x) = 0.0127 * x + 0.0000
  if 0.25 <= x <= 0.50:  u(x) = 0.0000 * x + 0.0032
  if 0.50 <= x <= 0.75:  u(x) = 0.0000 * x + 0.0032
  if 0.75 <= x <= 1.00:  u(x) = 0.0000 * x + 0.0032

Very High Hazard Severity Zones % within a Half Mile(x) =
  if 0.00 <= x <= 0.25:  u(x) = 1.5199 * x + 0.0000
  if 0.25 <= x <= 0.50:  u(x) = 0.0049 * x + 0.3787
  if 0.50 <= x <= 0.75:  u(x) = 0.0000 * x + 0.3812
  if 0.75 <= x <= 1.00:  u(x) = 0.0000 * x + 0.3812

Agriculture and Fuel Break % within a Half Mile(x) =
  if 0.00 <= x <= 0.25:  u(x) = 0.0000 * x + 0.0000
  if 0.25 <= x <= 0.50:  u(x) = 0.9673 * x + -0.2418
  if 0.50 <= x <= 0.75:  u(x) = 0.0000 * x + 0.2418
  if 0.75 <= x <= 1.00:  u(x) = 0.0000 * x + 0.2418

Burn Scar % within a Half Mile(x) =
  if 0.00 <= x <= 0.25:  u(x) = 0.0024 * x + 0.0000
  if 0.25 <= x <= 0.50:  u(x) = 0.0000 * x + 0.0006
  if 0.50 <= x <= 0.75:  u(x) = 0.0000 * x + 0.0006
  if 0.75 <= x <= 1.00:  u(x) = 0.0000 * x + 0.0006

Slope (%)(x) =
  if 0.00 <= x <= 0.25:  u(x) = 0.0102 * x + 0.0000
  if 0.25 <= x <= 0.50:  u(x) = 0.0000 * x + 0.0025
  if 0.50 <= x <= 0.75:  u(x) = 0.0000 * x + 0.0025
  if 0.75 <= x <= 1.00:  u(x) = 0.0000 * x + 0.0025

WUI Coverage % within a Half Mile(x) =
  if 0.00 <= x <= 0.25:  u(x) = 0.0000 * x + 0.0000
  if 0.25 <= x <= 0.50:  u(x) = 0.0000 * x + 0.0000
  if 0.50 <= x <= 0.75:  u(x) = 1.4802 * x + -0.7401
  if 0.75 <= x <= 1.00:  u(x) = 0.0000 * x + 0.3701

Fire Behavior Fuel Model (normalized)(x) =
  if 0.00 <= x <= 0.25:  u(x) = 0.0024 * x + 0.0000
  if 0.25 <= x <= 0.50:  u(x) = 0.0000 * x + 0.0006
  if 0.50 <= x <= 0.75:  u(x) = 0.0000 * x + 0.0006
  if 0.75 <= x <= 1.00:  u(x) = 0.0000 * x + 0.0006

Subset: subset_3

Best alpha: 4 | Breakpoints: [0.00, 0.25, 0.50, 0.75, 1.00]
AvgRank (Utilities): 14369.50 AvgRank (Linear): 17734.04 Top500 (U): 0.0% Top500 (W): 0.0%

Piecewise utility functions

utility plot

Linear weights

weights bar

Piecewise equations

Count of Structures within a Quarter Mile(x) =
  if 0.00 <= x <= 0.25:  u(x) = 0.0112 * x + 0.0000
  if 0.25 <= x <= 0.50:  u(x) = 0.0055 * x + 0.0014
  if 0.50 <= x <= 0.75:  u(x) = 0.0003 * x + 0.0040
  if 0.75 <= x <= 1.00:  u(x) = 0.0000 * x + 0.0042

Very High Hazard Severity Zones % within a Half Mile(x) =
  if 0.00 <= x <= 0.25:  u(x) = 0.0000 * x + 0.0000
  if 0.25 <= x <= 0.50:  u(x) = 0.0051 * x + -0.0013
  if 0.50 <= x <= 0.75:  u(x) = 0.0000 * x + 0.0013
  if 0.75 <= x <= 1.00:  u(x) = 0.0000 * x + 0.0013

Agriculture and Fuel Break % within a Half Mile(x) =
  if 0.00 <= x <= 0.25:  u(x) = 3.9659 * x + 0.0000
  if 0.25 <= x <= 0.50:  u(x) = 0.0026 * x + 0.9908
  if 0.50 <= x <= 0.75:  u(x) = 0.0000 * x + 0.9921
  if 0.75 <= x <= 1.00:  u(x) = 0.0000 * x + 0.9921

Burn Scar % within a Half Mile(x) =
  if 0.00 <= x <= 0.25:  u(x) = 0.0000 * x + 0.0000
  if 0.25 <= x <= 0.50:  u(x) = 0.0000 * x + 0.0000
  if 0.50 <= x <= 0.75:  u(x) = 0.0000 * x + 0.0000
  if 0.75 <= x <= 1.00:  u(x) = 0.0000 * x + 0.0000

Slope (%)(x) =
  if 0.00 <= x <= 0.25:  u(x) = 0.0000 * x + 0.0000
  if 0.25 <= x <= 0.50:  u(x) = 0.0017 * x + -0.0004
  if 0.50 <= x <= 0.75:  u(x) = 0.0000 * x + 0.0004
  if 0.75 <= x <= 1.00:  u(x) = 0.0000 * x + 0.0004

WUI Coverage % within a Half Mile(x) =
  if 0.00 <= x <= 0.25:  u(x) = 0.0000 * x + 0.0000
  if 0.25 <= x <= 0.50:  u(x) = 0.0000 * x + 0.0000
  if 0.50 <= x <= 0.75:  u(x) = 0.0000 * x + 0.0000
  if 0.75 <= x <= 1.00:  u(x) = 0.0010 * x + -0.0007

Fire Behavior Fuel Model (normalized)(x) =
  if 0.00 <= x <= 0.25:  u(x) = 0.0000 * x + 0.0000
  if 0.25 <= x <= 0.50:  u(x) = 0.0067 * x + -0.0017
  if 0.50 <= x <= 0.75:  u(x) = 0.0000 * x + 0.0017
  if 0.75 <= x <= 1.00:  u(x) = 0.0000 * x + 0.0017

Subset: subset_4

Best alpha: 3 | Breakpoints: [0.00, 0.33, 0.67, 1.00]
AvgRank (Utilities): 65.88 AvgRank (Linear): 139.70 Top500 (U): 100.0% Top500 (W): 97.7%

Piecewise utility functions

utility plot

Linear weights

weights bar

Piecewise equations

Count of Structures within a Quarter Mile(x) =
  if 0.00 <= x <= 0.33:  u(x) = 0.0097 * x + 0.0000
  if 0.33 <= x <= 0.67:  u(x) = 0.0000 * x + 0.0032
  if 0.67 <= x <= 1.00:  u(x) = 0.0109 * x + -0.0040

Very High Hazard Severity Zones % within a Half Mile(x) =
  if 0.00 <= x <= 0.33:  u(x) = 0.0000 * x + 0.0000
  if 0.33 <= x <= 0.67:  u(x) = 0.0000 * x + 0.0000
  if 0.67 <= x <= 1.00:  u(x) = 0.0000 * x + 0.0000

Agriculture and Fuel Break % within a Half Mile(x) =
  if 0.00 <= x <= 0.33:  u(x) = 2.0085 * x + 0.0000
  if 0.33 <= x <= 0.67:  u(x) = 0.0038 * x + 0.6683
  if 0.67 <= x <= 1.00:  u(x) = 0.0002 * x + 0.6706

Burn Scar % within a Half Mile(x) =
  if 0.00 <= x <= 0.33:  u(x) = 0.0000 * x + 0.0000
  if 0.33 <= x <= 0.67:  u(x) = 0.0000 * x + 0.0000
  if 0.67 <= x <= 1.00:  u(x) = 0.0000 * x + 0.0000

Slope (%)(x) =
  if 0.00 <= x <= 0.33:  u(x) = 0.0000 * x + 0.0000
  if 0.33 <= x <= 0.67:  u(x) = 0.0242 * x + -0.0081
  if 0.67 <= x <= 1.00:  u(x) = 0.0000 * x + 0.0081

WUI Coverage % within a Half Mile(x) =
  if 0.00 <= x <= 0.33:  u(x) = 0.0000 * x + 0.0000
  if 0.33 <= x <= 0.67:  u(x) = 0.9412 * x + -0.3137
  if 0.67 <= x <= 1.00:  u(x) = 0.0006 * x + 0.3133

Fire Behavior Fuel Model (normalized)(x) =
  if 0.00 <= x <= 0.33:  u(x) = 0.0007 * x + 0.0000
  if 0.33 <= x <= 0.67:  u(x) = 0.0000 * x + 0.0002
  if 0.67 <= x <= 1.00:  u(x) = 0.0000 * x + 0.0002

Subset: subset_5

Best alpha: 3 | Breakpoints: [0.00, 0.33, 0.67, 1.00]
AvgRank (Utilities): 205.74 AvgRank (Linear): 236.51 Top500 (U): 100.0% Top500 (W): 84.6%

Piecewise utility functions

utility plot

Linear weights

weights bar

Piecewise equations

Count of Structures within a Quarter Mile(x) =
  if 0.00 <= x <= 0.33:  u(x) = 0.0000 * x + 0.0000
  if 0.33 <= x <= 0.67:  u(x) = 2.9310 * x + -0.9770
  if 0.67 <= x <= 1.00:  u(x) = 0.0086 * x + 0.9713

Very High Hazard Severity Zones % within a Half Mile(x) =
  if 0.00 <= x <= 0.33:  u(x) = 0.0166 * x + 0.0000
  if 0.33 <= x <= 0.67:  u(x) = 0.0000 * x + 0.0055
  if 0.67 <= x <= 1.00:  u(x) = 0.0000 * x + 0.0055

Agriculture and Fuel Break % within a Half Mile(x) =
  if 0.00 <= x <= 0.33:  u(x) = 0.0000 * x + 0.0000
  if 0.33 <= x <= 0.67:  u(x) = 0.0392 * x + -0.0131
  if 0.67 <= x <= 1.00:  u(x) = 0.0000 * x + 0.0131

Burn Scar % within a Half Mile(x) =
  if 0.00 <= x <= 0.33:  u(x) = 0.0000 * x + 0.0000
  if 0.33 <= x <= 0.67:  u(x) = 0.0000 * x + 0.0000
  if 0.67 <= x <= 1.00:  u(x) = 0.0000 * x + 0.0000

Slope (%)(x) =
  if 0.00 <= x <= 0.33:  u(x) = 0.0000 * x + 0.0000
  if 0.33 <= x <= 0.67:  u(x) = 0.0000 * x + 0.0000
  if 0.67 <= x <= 1.00:  u(x) = 0.0000 * x + 0.0000

WUI Coverage % within a Half Mile(x) =
  if 0.00 <= x <= 0.33:  u(x) = 0.0000 * x + 0.0000
  if 0.33 <= x <= 0.67:  u(x) = 0.0000 * x + 0.0000
  if 0.67 <= x <= 1.00:  u(x) = 0.0000 * x + 0.0000

Fire Behavior Fuel Model (normalized)(x) =
  if 0.00 <= x <= 0.33:  u(x) = 0.0046 * x + 0.0000
  if 0.33 <= x <= 0.67:  u(x) = 0.0000 * x + 0.0015
  if 0.67 <= x <= 1.00:  u(x) = 0.0000 * x + 0.0015

Subset: subset_6

Best alpha: 4 | Breakpoints: [0.00, 0.25, 0.50, 0.75, 1.00]
AvgRank (Utilities): 1788.58 AvgRank (Linear): 3410.83 Top500 (U): 20.8% Top500 (W): 4.2%

Piecewise utility functions

utility plot

Linear weights

weights bar

Piecewise equations

Count of Structures within a Quarter Mile(x) =
  if 0.00 <= x <= 0.25:  u(x) = 0.0000 * x + 0.0000
  if 0.25 <= x <= 0.50:  u(x) = 0.0000 * x + 0.0000
  if 0.50 <= x <= 0.75:  u(x) = 0.0000 * x + 0.0000
  if 0.75 <= x <= 1.00:  u(x) = 0.0000 * x + 0.0000

Very High Hazard Severity Zones % within a Half Mile(x) =
  if 0.00 <= x <= 0.25:  u(x) = 0.0000 * x + 0.0000
  if 0.25 <= x <= 0.50:  u(x) = 0.0000 * x + 0.0000
  if 0.50 <= x <= 0.75:  u(x) = 0.0000 * x + 0.0000
  if 0.75 <= x <= 1.00:  u(x) = 0.0000 * x + 0.0000

Agriculture and Fuel Break % within a Half Mile(x) =
  if 0.00 <= x <= 0.25:  u(x) = 0.0000 * x + 0.0000
  if 0.25 <= x <= 0.50:  u(x) = 0.0000 * x + 0.0000
  if 0.50 <= x <= 0.75:  u(x) = 3.9777 * x + -1.9889
  if 0.75 <= x <= 1.00:  u(x) = 0.0000 * x + 0.9944

Burn Scar % within a Half Mile(x) =
  if 0.00 <= x <= 0.25:  u(x) = 0.0000 * x + 0.0000
  if 0.25 <= x <= 0.50:  u(x) = 0.0000 * x + 0.0000
  if 0.50 <= x <= 0.75:  u(x) = 0.0000 * x + 0.0000
  if 0.75 <= x <= 1.00:  u(x) = 0.0000 * x + 0.0000

Slope (%)(x) =
  if 0.00 <= x <= 0.25:  u(x) = 0.0093 * x + 0.0000
  if 0.25 <= x <= 0.50:  u(x) = 0.0000 * x + 0.0023
  if 0.50 <= x <= 0.75:  u(x) = 0.0000 * x + 0.0023
  if 0.75 <= x <= 1.00:  u(x) = 0.0000 * x + 0.0023

WUI Coverage % within a Half Mile(x) =
  if 0.00 <= x <= 0.25:  u(x) = 0.0000 * x + 0.0000
  if 0.25 <= x <= 0.50:  u(x) = 0.0000 * x + 0.0000
  if 0.50 <= x <= 0.75:  u(x) = 0.0000 * x + 0.0000
  if 0.75 <= x <= 1.00:  u(x) = 0.0000 * x + 0.0000

Fire Behavior Fuel Model (normalized)(x) =
  if 0.00 <= x <= 0.25:  u(x) = 0.0088 * x + 0.0000
  if 0.25 <= x <= 0.50:  u(x) = 0.0042 * x + 0.0011
  if 0.50 <= x <= 0.75:  u(x) = 0.0000 * x + 0.0032
  if 0.75 <= x <= 1.00:  u(x) = 0.0000 * x + 0.0032

Subset: subset_7

Best alpha: 3 | Breakpoints: [0.00, 0.33, 0.67, 1.00]
AvgRank (Utilities): 156.47 AvgRank (Linear): 616.47 Top500 (U): 100.0% Top500 (W): 64.7%

Piecewise utility functions

utility plot

Linear weights

weights bar

Piecewise equations

Count of Structures within a Quarter Mile(x) =
  if 0.00 <= x <= 0.33:  u(x) = 0.0084 * x + 0.0000
  if 0.33 <= x <= 0.67:  u(x) = 0.0000 * x + 0.0028
  if 0.67 <= x <= 1.00:  u(x) = 0.0000 * x + 0.0028

Very High Hazard Severity Zones % within a Half Mile(x) =
  if 0.00 <= x <= 0.33:  u(x) = 0.0000 * x + 0.0000
  if 0.33 <= x <= 0.67:  u(x) = 0.0000 * x + 0.0000
  if 0.67 <= x <= 1.00:  u(x) = 0.0000 * x + 0.0000

Agriculture and Fuel Break % within a Half Mile(x) =
  if 0.00 <= x <= 0.33:  u(x) = 0.0000 * x + 0.0000
  if 0.33 <= x <= 0.67:  u(x) = 0.0382 * x + -0.0127
  if 0.67 <= x <= 1.00:  u(x) = 0.0000 * x + 0.0127

Burn Scar % within a Half Mile(x) =
  if 0.00 <= x <= 0.33:  u(x) = 0.0302 * x + 0.0000
  if 0.33 <= x <= 0.67:  u(x) = 0.0000 * x + 0.0101
  if 0.67 <= x <= 1.00:  u(x) = 0.0000 * x + 0.0101

Slope (%)(x) =
  if 0.00 <= x <= 0.33:  u(x) = 0.0065 * x + 0.0000
  if 0.33 <= x <= 0.67:  u(x) = 0.0024 * x + 0.0014
  if 0.67 <= x <= 1.00:  u(x) = 0.0000 * x + 0.0030

WUI Coverage % within a Half Mile(x) =
  if 0.00 <= x <= 0.33:  u(x) = 0.0000 * x + 0.0000
  if 0.33 <= x <= 0.67:  u(x) = 2.9047 * x + -0.9682
  if 0.67 <= x <= 1.00:  u(x) = 0.0096 * x + 0.9618

Fire Behavior Fuel Model (normalized)(x) =
  if 0.00 <= x <= 0.33:  u(x) = 0.0000 * x + 0.0000
  if 0.33 <= x <= 0.67:  u(x) = 0.0000 * x + 0.0000
  if 0.67 <= x <= 1.00:  u(x) = 0.0000 * x + 0.0000

Subset: subset_8

Best alpha: 4 | Breakpoints: [0.00, 0.25, 0.50, 0.75, 1.00]
AvgRank (Utilities): 2334.43 AvgRank (Linear): 5046.62 Top500 (U): 0.0% Top500 (W): 0.0%

Piecewise utility functions

utility plot

Linear weights

weights bar

Piecewise equations

Count of Structures within a Quarter Mile(x) =
  if 0.00 <= x <= 0.25:  u(x) = 0.0008 * x + 0.0000
  if 0.25 <= x <= 0.50:  u(x) = 0.0000 * x + 0.0002
  if 0.50 <= x <= 0.75:  u(x) = 0.0000 * x + 0.0002
  if 0.75 <= x <= 1.00:  u(x) = 0.0000 * x + 0.0002

Very High Hazard Severity Zones % within a Half Mile(x) =
  if 0.00 <= x <= 0.25:  u(x) = 0.0000 * x + 0.0000
  if 0.25 <= x <= 0.50:  u(x) = 0.0000 * x + 0.0000
  if 0.50 <= x <= 0.75:  u(x) = 0.0000 * x + 0.0000
  if 0.75 <= x <= 1.00:  u(x) = 0.0000 * x + 0.0000

Agriculture and Fuel Break % within a Half Mile(x) =
  if 0.00 <= x <= 0.25:  u(x) = 2.1203 * x + 0.0000
  if 0.25 <= x <= 0.50:  u(x) = 0.0194 * x + 0.5252
  if 0.50 <= x <= 0.75:  u(x) = 0.0000 * x + 0.5349
  if 0.75 <= x <= 1.00:  u(x) = 0.0000 * x + 0.5349

Burn Scar % within a Half Mile(x) =
  if 0.00 <= x <= 0.25:  u(x) = 0.0096 * x + 0.0000
  if 0.25 <= x <= 0.50:  u(x) = 0.0000 * x + 0.0024
  if 0.50 <= x <= 0.75:  u(x) = 0.0000 * x + 0.0024
  if 0.75 <= x <= 1.00:  u(x) = 0.0000 * x + 0.0024

Slope (%)(x) =
  if 0.00 <= x <= 0.25:  u(x) = 0.0013 * x + 0.0000
  if 0.25 <= x <= 0.50:  u(x) = 0.0000 * x + 0.0003
  if 0.50 <= x <= 0.75:  u(x) = 0.0000 * x + 0.0003
  if 0.75 <= x <= 1.00:  u(x) = 0.0000 * x + 0.0003

WUI Coverage % within a Half Mile(x) =
  if 0.00 <= x <= 0.25:  u(x) = 0.0000 * x + 0.0000
  if 0.25 <= x <= 0.50:  u(x) = 0.0000 * x + 0.0000
  if 0.50 <= x <= 0.75:  u(x) = 1.8473 * x + -0.9237
  if 0.75 <= x <= 1.00:  u(x) = 0.0012 * x + 0.4609

Fire Behavior Fuel Model (normalized)(x) =
  if 0.00 <= x <= 0.25:  u(x) = 0.0000 * x + 0.0000
  if 0.25 <= x <= 0.50:  u(x) = 0.0000 * x + 0.0000
  if 0.50 <= x <= 0.75:  u(x) = 0.0000 * x + 0.0000
  if 0.75 <= x <= 1.00:  u(x) = 0.0000 * x + 0.0000

Subset: subset_9

Best alpha: 4 | Breakpoints: [0.00, 0.25, 0.50, 0.75, 1.00]
AvgRank (Utilities): 13428.68 AvgRank (Linear): 22571.39 Top500 (U): 0.0% Top500 (W): 0.0%

Piecewise utility functions

utility plot

Linear weights

weights bar

Piecewise equations

Count of Structures within a Quarter Mile(x) =
  if 0.00 <= x <= 0.25:  u(x) = 0.0000 * x + 0.0000
  if 0.25 <= x <= 0.50:  u(x) = 0.0000 * x + 0.0000
  if 0.50 <= x <= 0.75:  u(x) = 0.0000 * x + 0.0000
  if 0.75 <= x <= 1.00:  u(x) = 0.0000 * x + 0.0000

Very High Hazard Severity Zones % within a Half Mile(x) =
  if 0.00 <= x <= 0.25:  u(x) = 0.0000 * x + 0.0000
  if 0.25 <= x <= 0.50:  u(x) = 0.0000 * x + 0.0000
  if 0.50 <= x <= 0.75:  u(x) = 0.0000 * x + 0.0000
  if 0.75 <= x <= 1.00:  u(x) = 0.0000 * x + 0.0000

Agriculture and Fuel Break % within a Half Mile(x) =
  if 0.00 <= x <= 0.25:  u(x) = 2.2491 * x + 0.0000
  if 0.25 <= x <= 0.50:  u(x) = 0.0000 * x + 0.5623
  if 0.50 <= x <= 0.75:  u(x) = 0.0000 * x + 0.5623
  if 0.75 <= x <= 1.00:  u(x) = 0.0000 * x + 0.5623

Burn Scar % within a Half Mile(x) =
  if 0.00 <= x <= 0.25:  u(x) = 0.0000 * x + 0.0000
  if 0.25 <= x <= 0.50:  u(x) = 0.0000 * x + 0.0000
  if 0.50 <= x <= 0.75:  u(x) = 0.0000 * x + 0.0000
  if 0.75 <= x <= 1.00:  u(x) = 0.0000 * x + 0.0000

Slope (%)(x) =
  if 0.00 <= x <= 0.25:  u(x) = 0.0000 * x + 0.0000
  if 0.25 <= x <= 0.50:  u(x) = 0.0000 * x + 0.0000
  if 0.50 <= x <= 0.75:  u(x) = 0.0000 * x + 0.0000
  if 0.75 <= x <= 1.00:  u(x) = 0.0000 * x + 0.0000

WUI Coverage % within a Half Mile(x) =
  if 0.00 <= x <= 0.25:  u(x) = 0.0000 * x + 0.0000
  if 0.25 <= x <= 0.50:  u(x) = 0.0000 * x + 0.0000
  if 0.50 <= x <= 0.75:  u(x) = 1.7509 * x + -0.8754
  if 0.75 <= x <= 1.00:  u(x) = 0.0000 * x + 0.4377

Fire Behavior Fuel Model (normalized)(x) =
  if 0.00 <= x <= 0.25:  u(x) = 0.0000 * x + 0.0000
  if 0.25 <= x <= 0.50:  u(x) = 0.0000 * x + 0.0000
  if 0.50 <= x <= 0.75:  u(x) = 0.0000 * x + 0.0000
  if 0.75 <= x <= 1.00:  u(x) = 0.0000 * x + 0.0000

Final Summary Table (All Subsets)

subset approach qtrmi_s hvhsz_s agfb_s hbrn_s slope_s hwui_s fbfm_s avg min max top500 utilbp_qtrmi_s_0 utilbp_qtrmi_s_1 utilbp_qtrmi_s_2 utilbp_qtrmi_s_3 utilbp_qtrmi_s_4 utilbp_hvhsz_s_0 utilbp_hvhsz_s_1 utilbp_hvhsz_s_2 utilbp_hvhsz_s_3 utilbp_hvhsz_s_4 utilbp_agfb_s_0 utilbp_agfb_s_1 utilbp_agfb_s_2 utilbp_agfb_s_3 utilbp_agfb_s_4 utilbp_hbrn_s_0 utilbp_hbrn_s_1 utilbp_hbrn_s_2 utilbp_hbrn_s_3 utilbp_hbrn_s_4 utilbp_slope_s_0 utilbp_slope_s_1 utilbp_slope_s_2 utilbp_slope_s_3 utilbp_slope_s_4 utilbp_hwui_s_0 utilbp_hwui_s_1 utilbp_hwui_s_2 utilbp_hwui_s_3 utilbp_hwui_s_4 utilbp_fbfm_s_0 utilbp_fbfm_s_1 utilbp_fbfm_s_2 utilbp_fbfm_s_3 utilbp_fbfm_s_4
parcels_subset piecewise 0.547140 0.001000 0.000000 0.019339 0.001584 0.000000 0.430937 2194.176471 81 6119 2 0.0 0.000000 0.000000 0.000000 0.547140 0.0 0.000000 0.000000 0.001000 0.001000 0.0 0.000000 0.000000 0.000000 0.000000 0.0 0.019339 0.019339 0.019339 0.019339 0.0 0.001584 0.001584 0.001584 0.001584 0.0 0.000000 0.000000 0.000000 0.000000 0.0 0.430937 0.430937 0.430937 0.430937
parcels_subset linear 0.183851 0.114217 0.000000 0.467179 0.070023 0.000000 0.164730 3674.058824 179 11287 2 NaN NaN NaN NaN NaN NaN NaN NaN NaN NaN NaN NaN NaN NaN NaN NaN NaN NaN NaN NaN NaN NaN NaN NaN NaN NaN NaN NaN NaN NaN NaN NaN NaN NaN NaN
subset_1 piecewise 0.009018 0.000000 0.030176 0.954284 0.000000 0.005553 0.000969 25.764706 5 80 17 0.0 0.009018 0.009018 NaN NaN 0.0 0.000000 0.000000 NaN NaN 0.0 0.000000 0.030176 NaN NaN 0.0 0.949421 0.954284 NaN NaN 0.0 0.000000 0.000000 NaN NaN 0.0 0.001077 0.005553 NaN NaN 0.0 0.000969 0.000969 NaN NaN
subset_1 linear 0.046250 0.000000 0.711954 0.176169 0.000000 0.065627 0.000000 29.941176 7 86 17 NaN NaN NaN NaN NaN NaN NaN NaN NaN NaN NaN NaN NaN NaN NaN NaN NaN NaN NaN NaN NaN NaN NaN NaN NaN NaN NaN NaN NaN NaN NaN NaN NaN NaN NaN
subset_2 piecewise 0.003164 0.381216 0.241815 0.000602 0.002548 0.370050 0.000605 899.083333 159 2636 11 0.0 0.003164 0.003164 0.003164 0.003164 0.0 0.379981 0.381216 0.381216 0.381216 0.0 0.000000 0.241815 0.241815 0.241815 0.0 0.000602 0.000602 0.000602 0.000602 0.0 0.002548 0.002548 0.002548 0.002548 0.0 0.000000 0.000000 0.370050 0.370050 0.0 0.000605 0.000605 0.000605 0.000605
subset_2 linear 0.160809 0.305117 0.113166 0.000000 0.126600 0.294308 0.000000 2520.500000 853 4530 0 NaN NaN NaN NaN NaN NaN NaN NaN NaN NaN NaN NaN NaN NaN NaN NaN NaN NaN NaN NaN NaN NaN NaN NaN NaN NaN NaN NaN NaN NaN NaN NaN NaN NaN NaN
subset_3 piecewise 0.004241 0.001276 0.992131 0.000000 0.000437 0.000247 0.001667 14369.500000 563 37062 0 0.0 0.002788 0.004164 0.004241 0.004241 0.0 0.000000 0.001276 0.001276 0.001276 0.0 0.991481 0.992131 0.992131 0.992131 0.0 0.000000 0.000000 0.000000 0.000000 0.0 0.000000 0.000437 0.000437 0.000437 0.0 0.000000 0.000000 0.000000 0.000247 0.0 0.000000 0.001667 0.001667 0.001667
subset_3 linear 0.346646 0.024967 0.047711 0.449907 0.040436 0.000000 0.090333 17734.041667 2288 47043 0 NaN NaN NaN NaN NaN NaN NaN NaN NaN NaN NaN NaN NaN NaN NaN NaN NaN NaN NaN NaN NaN NaN NaN NaN NaN NaN NaN NaN NaN NaN NaN NaN NaN NaN NaN
subset_4 piecewise 0.006878 0.000000 0.670849 0.000000 0.008080 0.313949 0.000244 65.883721 2 242 43 0.0 0.003238 0.003238 0.006878 NaN 0.0 0.000000 0.000000 0.000000 NaN 0.0 0.669511 0.670771 0.670849 NaN 0.0 0.000000 0.000000 0.000000 NaN 0.0 0.000000 0.008080 0.008080 NaN 0.0 0.000000 0.313745 0.313949 NaN 0.0 0.000244 0.000244 0.000244 NaN
subset_4 linear 0.243458 0.000000 0.069757 0.000000 0.480166 0.196271 0.010349 139.697674 7 742 42 NaN NaN NaN NaN NaN NaN NaN NaN NaN NaN NaN NaN NaN NaN NaN NaN NaN NaN NaN NaN NaN NaN NaN NaN NaN NaN NaN NaN NaN NaN NaN NaN NaN NaN NaN
subset_5 piecewise 0.979874 0.005529 0.013058 0.000000 0.000000 0.000000 0.001539 205.743590 7 423 39 0.0 0.000000 0.977010 0.979874 NaN 0.0 0.005529 0.005529 0.005529 NaN 0.0 0.000000 0.013058 0.013058 NaN 0.0 0.000000 0.000000 0.000000 NaN 0.0 0.000000 0.000000 0.000000 NaN 0.0 0.000000 0.000000 0.000000 NaN 0.0 0.001539 0.001539 0.001539 NaN
subset_5 linear 0.529374 0.289022 0.000000 0.000000 0.105256 0.000000 0.076348 236.512821 1 836 33 NaN NaN NaN NaN NaN NaN NaN NaN NaN NaN NaN NaN NaN NaN NaN NaN NaN NaN NaN NaN NaN NaN NaN NaN NaN NaN NaN NaN NaN NaN NaN NaN NaN NaN NaN
subset_6 piecewise 0.000000 0.000000 0.994436 0.000000 0.002320 0.000000 0.003244 1788.583333 59 4003 5 0.0 0.000000 0.000000 0.000000 0.000000 0.0 0.000000 0.000000 0.000000 0.000000 0.0 0.000000 0.000000 0.994436 0.994436 0.0 0.000000 0.000000 0.000000 0.000000 0.0 0.002320 0.002320 0.002320 0.002320 0.0 0.000000 0.000000 0.000000 0.000000 0.0 0.002197 0.003244 0.003244 0.003244
subset_6 linear 0.000000 0.000000 0.570261 0.000000 0.205618 0.000000 0.224121 3410.833333 437 9393 1 NaN NaN NaN NaN NaN NaN NaN NaN NaN NaN NaN NaN NaN NaN NaN NaN NaN NaN NaN NaN NaN NaN NaN NaN NaN NaN NaN NaN NaN NaN NaN NaN NaN NaN NaN
subset_7 piecewise 0.002786 0.000000 0.012731 0.010062 0.002982 0.971439 0.000000 156.470588 24 424 17 0.0 0.002786 0.002786 0.002786 NaN 0.0 0.000000 0.000000 0.000000 NaN 0.0 0.000000 0.012731 0.012731 NaN 0.0 0.010062 0.010062 0.010062 NaN 0.0 0.002168 0.002982 0.002982 NaN 0.0 0.000000 0.968237 0.971439 NaN 0.0 0.000000 0.000000 0.000000 NaN
subset_7 linear 0.055114 0.000000 0.123436 0.220579 0.146356 0.454515 0.000000 616.470588 149 2071 11 NaN NaN NaN NaN NaN NaN NaN NaN NaN NaN NaN NaN NaN NaN NaN NaN NaN NaN NaN NaN NaN NaN NaN NaN NaN NaN NaN NaN NaN NaN NaN NaN NaN NaN NaN
subset_8 piecewise 0.000194 0.000000 0.534939 0.002396 0.000335 0.462136 0.000000 2334.428571 1712 3202 0 0.0 0.000194 0.000194 0.000194 0.000194 0.0 0.000000 0.000000 0.000000 0.000000 0.0 0.530083 0.534939 0.534939 0.534939 0.0 0.002396 0.002396 0.002396 0.002396 0.0 0.000335 0.000335 0.000335 0.000335 0.0 0.000000 0.000000 0.461832 0.462136 0.0 0.000000 0.000000 0.000000 0.000000
subset_8 linear 0.036156 0.000000 0.000000 0.400499 0.000000 0.563345 0.000000 5046.619048 2979 8531 0 NaN NaN NaN NaN NaN NaN NaN NaN NaN NaN NaN NaN NaN NaN NaN NaN NaN NaN NaN NaN NaN NaN NaN NaN NaN NaN NaN NaN NaN NaN NaN NaN NaN NaN NaN
subset_9 piecewise 0.000000 0.000000 0.562276 0.000000 0.000000 0.437724 0.000000 13428.684211 8395 15993 0 0.0 0.000000 0.000000 0.000000 0.000000 0.0 0.000000 0.000000 0.000000 0.000000 0.0 0.562276 0.562276 0.562276 0.562276 0.0 0.000000 0.000000 0.000000 0.000000 0.0 0.000000 0.000000 0.000000 0.000000 0.0 0.000000 0.000000 0.437724 0.437724 0.0 0.000000 0.000000 0.000000 0.000000
subset_9 linear 0.287272 0.000000 0.000000 0.420331 0.000000 0.292397 0.000000 22571.394737 22178 23124 0 NaN NaN NaN NaN NaN NaN NaN NaN NaN NaN NaN NaN NaN NaN NaN NaN NaN NaN NaN NaN NaN NaN NaN NaN NaN NaN NaN NaN NaN NaN NaN NaN NaN NaN NaN

Friendly Overview

Subset Approach AvgRank MinRank MaxRank Top500 DominantCriterion DominantWeight SecondCriterion SecondWeight
parcels_subset Piecewise 2194.176471 81 6119 2 qtrmi_s 0.547140 fbfm_s 0.430937
parcels_subset Linear 3674.058824 179 11287 2 hbrn_s 0.467179 qtrmi_s 0.183851
subset_1 Piecewise 25.764706 5 80 17 hbrn_s 0.954284 agfb_s 0.030176
subset_1 Linear 29.941176 7 86 17 agfb_s 0.711954 hbrn_s 0.176169
subset_2 Piecewise 899.083333 159 2636 11 hvhsz_s 0.381216 hwui_s 0.370050
subset_2 Linear 2520.500000 853 4530 0 hvhsz_s 0.305117 hwui_s 0.294308
subset_3 Piecewise 14369.500000 563 37062 0 agfb_s 0.992131 qtrmi_s 0.004241
subset_3 Linear 17734.041667 2288 47043 0 hbrn_s 0.449907 qtrmi_s 0.346646
subset_4 Piecewise 65.883721 2 242 43 agfb_s 0.670849 hwui_s 0.313949
subset_4 Linear 139.697674 7 742 42 slope_s 0.480166 qtrmi_s 0.243458
subset_5 Piecewise 205.743590 7 423 39 qtrmi_s 0.979874 agfb_s 0.013058
subset_5 Linear 236.512821 1 836 33 qtrmi_s 0.529374 hvhsz_s 0.289022
subset_6 Piecewise 1788.583333 59 4003 5 agfb_s 0.994436 fbfm_s 0.003244
subset_6 Linear 3410.833333 437 9393 1 agfb_s 0.570261 fbfm_s 0.224121
subset_7 Piecewise 156.470588 24 424 17 hwui_s 0.971439 agfb_s 0.012731
subset_7 Linear 616.470588 149 2071 11 hwui_s 0.454515 hbrn_s 0.220579
subset_8 Piecewise 2334.428571 1712 3202 0 agfb_s 0.534939 hwui_s 0.462136
subset_8 Linear 5046.619048 2979 8531 0 hwui_s 0.563345 hbrn_s 0.400499
subset_9 Piecewise 13428.684211 8395 15993 0 agfb_s 0.562276 hwui_s 0.437724
subset_9 Linear 22571.394737 22178 23124 0 hbrn_s 0.420331 hwui_s 0.292397